Another idea to further explore the profound connection between spacetime geometry and quantum entanglement is inspired by the optimization problem in network flow theory. [1]}, [2]}, [3]} developed the optimization theory of flows on manifolds, endowed with the name of “bit threads", and proposed the concept of bit threads can equivalently formulate the RT formula. In this letter, by studying the connection between bit threads and SS duality, we propose a natural and novel physical property of bit threads, dubbed “thread/state correspondence”, that is, in a so-called locking bit thread configuration [4]}, [5]}, [6]}, [7]}, each bit thread is in a quantum superposition state of two orthogonal states. Since the flux of bit threads is directly related to the geometry of a holographic spacetime, while this thread-state property can cleverly characterize quantum entanglement as one will see, it can be expected to be a very useful advance in the study of the relationship between quantum entanglement and spacetime geometry. Note that because bit threads are visually intuitive, they have usually been interpreted implicitly as the bell pairs distilled from the boundary quantum systems, however, they are mostly used merely as a mathematical tool to study different aspects of the holographic principle (see e.g. [7]}, [6]}, [5]}, [4]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}). Our thread/state rules explicitly accentuate for the first time the implied meaning of the name “bit threads”, namely, that these threads, which are used mathematically to recover the RT formula, can be physically assigned a meaning closely related to the concept of “bits”.
